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[Reprinted  from  Journal  of  Experimental  Psychology,  Vol.  I,  No.  2.  Apr..  1916. 


UNIVERSITY  of  CALlFOlRim 

AT 

LOS  ANGELES 

4.IBRARY 


THE  CONSTANT  ERROR  OF  TOUCH  LOCALIZATION 

BY  SHEPHERD  IVORY  FRANZ 

In  the  consideration  of  the  ability  of  localization  on  the 
skin  of  points  stimulated  by  light  touches,  by  pressures,  by 
pain  stimuli,  and  by  temperature  stimuli,  the  conclusions 
of  Ponzo^  have  been  widely  quoted  and  accepted.-  The 
conclusions  set  forth  by  Ponzo  in  his  various  articles  are, 
as  I  have  shown  in  a  previous  publication,'  open  to  question 
in  certain  particulars,  and  it  is  with  regard  to  his  conclusions 
respecting  the  constant  error  that  the  present  paper  is  pre- 
sented. It  is  convenient  to  deal  with  these  matters  under 
the  two  headings  of  method  and  facts. 

Method. — The  usual  method  of  determining  the  constant 
error  in  experiments  of  this  character  is  familiar  to  all  who 
have  investigated  these  matters.  It  does  not  need  to  detain 
us  long  at  this  time.  Briefly  the  constant  error  is  found  in 
the  following  manner:  The  tendency  to  the  localization  of 
points  in  a  special  direction  is  determined  by  referring  the 
localizations  to  predetermined  axes  of  ordinates  which  meet 
at  the  point  of  reference  or  origin  of  coordinates,  which  in 
touch  localization  tests  is  the  point  stimulated.  The  points 
localiyed  to  the  right  and  those  to  the  left  of  the  vertical 
axis  are  considered  algebraic  opposites,  and  similarly  those 

1  M.  Ponzo,  'Recherches  sur  la  localisation  des  sensations  tactiles  et  des  sensations 
dolorifiuues,'  Arch.  ital.  de  biol.,  191 1,  55,  I-14. 

*  Seo,  for  example,  the  reviews  of  H.  D.  Cook  in  Psychol.  Bull.,  1913,  10,  258-261; 
1914,  n,  238-241. 

»  S.  I.  Franz,  'The  Accuracy  of  Localization  of  Touch  Stimuli  on  Different  Bodily- 
Segments,'  Psychol.  Rev.,  1913,  20,  107-128. 

1248  ■;■  n 


84  S.  /.  FRANZ 

above  and  those  below  the  horizontal  axis.  The  averages 
of  the  algebraic  sums  will  give  the  location  of  the  average 
tendency,  or  the  average  constant  error,^ 

Ponzo's  method  of  determining  the  constant  error  is, 
superficially,  one  of  great  simplicity,  and  of  apparent  value. 
Briefly  in  relation  to  the  localization  of  the  skin  sensations 
it  is  as  follows:  Either  before  or  after  the  performance  of 
a  series  of  tests  a  primary  axis  is  drawn  through  the  point  of 
stimulation  to  represent  the  supposed  direction  of  the  nerve 
or  other  anatomical  segmental  axis;  through  the  point  two 
perpendicular  lines  are  drawn  in  such  a  fashion  that  each 
cuts  the  primary  axis  at  an  angle  of  45  degrees;  the  right 
angles  which  include  the  primary  axis  are  then  considered 
by  Ponzo  to  be  boundaries  to  those  points  which  are  in  the 
direction  of  the  primary  axis  and,  consequently,  to  be  in  the 
direction  of  the  anatomical  part.  All  localizations  falling 
within  these  boundaries  are  considered  to  be  "in  the  direction 
of  the  primary  axis." 

A  brief  consideration  will  show  that  by  the  use  of  Ponzo's 
method  conclusions  may  be  reached  which  are  neither  accurate 
nor  representative  of  the  actual  conditions.  The  extreme 
case  of  the  points  of  localization  falling  close  to  one  of  the 
boundaries  or  axes  of  reference  might  show  the  constant 
error  falling  within  the  direction  of  the  primary  axis,  and 
with  a  slight  shifting  of  the  points  the  constant  error  may 
be  found  to  be  in  a  direction  at  right  angles  to  the  primary 
axis.  Ponzo's  method  breaks  down  in  these  extreme  cases, 
and  in  cases  which  are  not  extremes.  If  the  latter  can  be 
shown,  we  should  conclude  that  the  method  is  not  sufficiently 
exact,  and  that  conclusions  based  upon  the  method  should 
not  be  accepted  until  they  have  been  confirmed  by  facts 
obtained  by  further  and  more  exact  methods.  Two  illustra- 
tions will  suffice  to  indicate  the  discrepancies  in  the  conclu- 
sions to  be  drawn  from  certain  results  when  the  two  methods 
of  determining  the  constant  error  are  used.  The  results 
which  give  these  illustrations   are  shown  in  Figs,    i    and   2. 

^  These  matters  are  so  elementary  that  at  first  sight  it  seems  superfluous  to  men- 
tion them,  but  the  acceptance  of  Ponzo's  conclusions,  without  due  criticism,  would 
indicate  the  necessity  for  repetition. 


CONSTANT  ERROR 


85 


They  show  the  localizations  of  a  subject  when  two  points 
on  the  mid-body  lines  were  stimulated. 


Figs,  i  and  2.  Results  of  experiments  on  the  localization  of  tactile  stimuli. 
The  points  stimulated  are  at  the  intersections  of  the  lines.  The  dotted  lines  show 
the  principal  axes,  full  lines,  the  general  directions  according  to  Ponzo.  Each  localiza- 
tion is  shown  as  a  point,  the  location  of  the  average  constant  error  as  an  encircled 
cross.     Twenty  tests  in  each  experiment.     For  further  details  see  texts. 

In  these  diagrams  the  primary  axis  is  shown  by  a  broken 
line  (with  arrow  markings),  and  Ponzo's  constant  error 
indicators  are  shown  as  unbroken  lines.  Each  point  of  local- 
ization is  shown  as  a  dot,  there  being  twenty  in  each  illustra- 
tion. Both  experiments  show  according  to  Ponzo's  method 
a  superiority  of  localization  in  the  direction  of  the  primary 
axis.  In  Fig.  i  the  number  of  points  in  the  space  315°  to- 
45°  is  10,  and  in  the  corresponding  space,  135°  to  225°,  2; 
the  numbers  in  the  perpendicular  spaces,  45°  to  135°  and 
225°  to  315°  being  8  and  o  respectively.  In  Fig.  2  the  points 
in  the  principal  directions,  315°  to  45°  and  135°  to  225°, 
are  5  and  7  respectively,  while  in  the  perpendicular  spaces, 
45°  to  135°  and  225°  to  315°,  there  are  i  and  7  respectively. 
In  each  of  these  experiments,  therefore,  there  are  12  points 
in  the  direction  of  the  principal  axis  and  8  points  not  in  that 
direction.     It   will   thus   be  seen   that  there  is   an   apparent 


86  S.  /.   FRANZ 

constant  error  (by  Ponzo's  method)  In  the  direction  of  the 
principal  axis,  the  number  of  such  localizations  being  fifty 
per  cent,  more  than  In  the  other  direction. 

When  the  results  In  these  two  experiments  are  calculated 
by  the  usual  method  of  determining  the  constant  error  the 
supposed  tendency  to  locate  along  the  principal  axis  is  not 
found  to  be  present.  Thus,  the  results  In  Fig.  i  show  an 
average  constant  error  toward  the  right  of  15.2  mm.  and  an 
upward  tendency  of  10.6  mm.  The  results  In  Fig.  2  show 
an  average  constant  error  of  n.2  mm.  to  the  left  and  1.9  mm. 
downward.  The  localizations  of  these  average  constant 
errors  are  shown  by  small  encircled  crosses. 

It  will  be  seen,  therefore,  that  although  by  Ponzo's  method 
the  constant  error  In  these  two  examples  Is  the  same,  this 
error  when  determined  by  the  usual  method  differs  In  the 
two  cases.  In  the  first  example  it  Is  toward  the  right,  in  the 
second  It  is  toward  the  left.  In  the  first  example  the  con- 
stant error  Is  at  an  angle  of  55.5  degrees  from  the  upper  part 
of  the  principal  line,  In  the  second  it  is  at  an  angle  of  260 
degrees.^  In  each  case  the  "angular"  error  does  not  He 
within  the  angular  limits  which  Ponzo  sets  as  the  direction 
or  axis  of  the  anatomical  part. 

An  objection  may  be  raised  that  the  Illustrated  examples 
are  Isolated  and  extremes,  and  that  they  do  not  fairly  repre- 
sent the  conditions  with  which  Ponzo,  in  his  work,  and  I,  in 
my  former  paper,  dealt.  In  a  brief  space  it  is  not  possible 
to  discuss  In  detail  the  results  which  Ponzo  has  reported  and 
illustrated,  but  examples  In  which  similar,  but  perhaps  not 
as  extensive,  differences  are  to  be  found  are  given  in  Ponzo's 
publications.  At  the  same  time  It  may  be  stated  that  the 
results  on  the  individual  points  which  were  grouped  in  my 
previous  article  show  at  times  as  great  deviations  as  in  the 
two  examples  given  here.  Because  of  these  variations  In  a 
number  of  tests  on  different  days  the  average  constant  error 
for  one  point  or  for  an  anatomical  segment  is  not  large. 
Furthermore  It  should  be  stated  that  if  the  method  of  Ponzo 

^  Both  roughly  measured  by  a  protractor  showing  angular  degrees,  and  using  the 
vertical  axis  above  the  stimulated  point  as  zero  degrees. 


CONSTANT  ERROR  87 

breaks  down  in  cases  of  this  character,  which  I  cannot  con- 
sider to  be  extremes,  it  is  a  method  upon  which  little  or  no 
reliance  can  be  placed,  especially  when  broad  generalizations 
are  to  follow  from  the  account  of  the  results. 

Facts. — A  question  immediately  arises  regarding  the 
accuracy  of  Ponzo's  statement  of  the  conditions  encountered 
in  localization  tests  when  the  adequacy  of  his  method  of 
dealing  with  the  observations  is  disputed.  Are  suppositious 
general  tendencies  toward  localizations  along  certain  bodily 
axes,  or  along  the  courses  of  nerves,  dependent  upon  his 
erroneous  method  of  calculation  of  the  constant  error,  or  are 
they  found  to  exist  when  the  usual  and  more  accurate  constant 
error  method  is  employed.^  An  answer  to  this  question  is 
given  in  part  in  my  previous  paper,  although  in  that  article 
the  results  of  the  constant  errors  of  localizations  of  touch 
stimuli  for  individual  points  were  not  given  in  full.  The  fact 
that  my  results  on  the  individual  points  were  not  reported 
has  led  some  to  believe  that  my  groupings  into  larger  anatomi- 
cal segments  have  concealed  or  balanced  the  constant  errors, 
and  that  the  apparent  discrepancies  between  Ponzo's  and  my 
conclusions  would  disappear  if  I  had  dealt  with  the  individual 
points.  A  further  consideration  of  the  groupings  and  the 
results  from  them  will,  however,  serve  to  show  that  such 
is  not  entirely,  if  at  all,  the  case.  If  similar  groupings  are 
made  for  all  subjects  the  results  should  be  directly  com- 
parable, regardless  of  the  kinds  of  groupings,  and  it  would 
make  no  difference  how  large  or  how  small  a  grouping  is 
made.  That  the  constant  errors  are  not  the  same  in  the  two 
subjects,  A  and  C,  whose  results  were  published,  is  evident 
from  inspection.^  At  the  same  time  it  must  be  observed 
that  with  the  groupings  in  the  two  series  of  the  same  subject, 
A^  the  constant  errors  were  not  always  the  same.  Other 
results  to  which  I  may  refer  are  those  for  the  soles  of  the  feet 
of  these  two  subjects,  on  each  of  which  anatomical  part  only 
one  point  of  stimulation  was  used.  The  results  of  the  two 
series  of  tests  on  subject  A  do  not  correspond,  although  the 
results  with  subject  C  have  a  fairly  close  correspondence  with 

'  See  Table  V.,  page  120  of  my  previous  article,  op.  cit. 


88  S.  /.  FRANZ 

the  results  of  the  first  series  on  subject  A}  In  this  connec- 
tion attention  may  be  called  to  the  results  obtained  by 
another  method  of  constant  error  estimation  which  I  em- 
ployed and  which  gave  inconstant  results.  When  the  subject 
localized  the  first  stimulation  this  localization  was  taken  as 
the  second  point  of  stimulation,  the  second  localization  was 
taken  as  the  third  point  of  stimulation,  etc.  Subject  A  by 
this  method,  starting  from  a  point  on  the  mid-line  of  the  body 
and  on  a  level  with  the  nipples,  reached  in  lo  tests  on  one 
day  "a  point  8.5  cm.  from  the  mid-line  and  17  cm.  below  the 
first  stimulation.  ...  In  a  second  experiment  on  a  subse- 
quent day  in  10  tests  the  point  was  reached  on  the  left  10  cm. 
from  the  mid-line  and  16.5  cm.  below  the  first  stimulation. 
In  a  third  series,  a  point  was  reached  after  10  tests,  11  cm. 
from  the  mid-line,  and  9  cm.  below  the  first  stimulus."^  In 
relation  to  the  primary  points  the  general  tendencies  in  these 
three  tests  are  indicated  by  the  angular  relations  of  the 
average  constant  errors  to  the  point  on  the  mid-line.  These 
are  respectively  153,  148,  and  129  degrees.^  The  approxi- 
mate amount  of  the  angle  of  the  ribs  with  the  sternum  at 
the  original  point  of  stimulation  is  approximately  85  degrees. 
These  results  tend  to  confirm  what  I  shall  now  endeavor  to 
show  more  accurately,  namely,  that  the  errors  of  localization 
of  stimuli  to  definite  points  in  certain  anatomical  segments 

1  It  would  not  be  justifiable  to  make  further  comparisons  of  supposedly  similar 
points  on  different  subjects  at  this  time,  for  it  is  not  possible  to  determine  that  the 
points  were  in  all  cases  anatomically  identically  located.  The  subjects  are  no  longer 
available  (artists'  models  make  up  part  of  our  city-to-city  floating  population)  and 
anatomical  comparisons  cannot  be  made.  The  reason  why  this  comparison  cannot 
be  made  from  my  available  records  is  because  I  selected  for  my  former  work  points 
w-hich  were  at  definite  distances  from  certain  anatomical  landmarks,  such  as  the 
axilla,  the  umbilicus,  the  nipples,  etc.,  but  with  the  differences  in  lengths  and  girths 
of  the  bodies  the  points  did  not  always  correspond  with  respect  to  other  bony  land- 
marks and  with  the  supposed  courses  of  nerves.  Especially  in  relation  to  the  stimu- 
lated points  on  the  thorax  are  these  differences  of  importance,  for  a  variation  of  one 
or  two  centimeters  in  the  length  of  the  chest  would  shift  the  location  of  a  point  from 
an  intercostal  space  to  a  supracostal  area,  or  vice  versa.  The  recalculation  of  the 
individual  points  would  not,  therefore,  be  of  any  advantage  towards  the  solution  of 
the  problem. 

^  Op.  cit.,  p.  121. 

*  Protractor  measurements. 


CONSTANT  ERROR  89 

do  not  correspond  with  the  direction  of  the  nerves,  as  Ponzo 
has  contended. 

Ponzo's^  conclusions  on  this  point  refer  especially  to  the 
localization  of  pressure  and  pain  stimuli  in  the  intercostal 
spaces.  He  has  reported  for  three  subjects  results  of  localiza- 
tion of  stimuli  in  the  fifth,  sixth,  seventh,  and  eighth  inter- 
costal spaces,  which  are  interpreted  to  indicate  a  localization 
in  the  direction  of  the  intercostal  spaces,  with  the  further 
tendency  to  locate  toward  the  end  branches  of  the  nerve 
which  innervates  the  skin  covering  such  a  space.  He  subse- 
quently added  the  conclusion  that  the  errors  of  localization 
of  sensations  of  warmth  and  of  cold  on  other  bodily  parts 
correspond  with  the  general  direction  of  the  superficial  nerve 
trunks.^  The  value  of  these  conclusions,  if  they  should  be 
found  to  be  correct,  is  very  great  for  anatomical  workers, 
but  greater  for  clinicians  who,  by  the  application  of  a  few 
tests  to  show  the  constant  error  in  the  localization  of  pressures 
and  temperature  stimuli,  would  be  enabled  to  discover  in  the 
living  subject  the  course  of  the  cutaneous  nerves  in  different 
portions  of  the  body. 

The  present  series  of  tests  were  made  upon  an  artists' 
model,  Miss  W.,  who  is  about  20  years  of  age.^  Special 
attention  was  paid  to  certain  areas  of  the  body  in  which  the 
directions  of  the  nerves  are  very  constant,  in  order  that  the 
constant  error  tendencies  might  be  considered  in  relation 
to  the  courses  of  these  nerves.  The  areas  which  were  in- 
vestigated are  as  follows:  {A)  A  point  in  the  axillary  line 
overlying  the  seventh  intercostal  space  when  the  arm  is  lying 
fairly  close  to  the  body;  {B)  a  point  near  the  mid-line  of 
the  chest  at  the  junction  of  the  fourth  intercostal  space  with 
the  sternum;  (C)  a  point  on  the  mid-body  line,  at  the  level 
of  the  nipples;  {D)  a  point  on  the  anterior  part  of  the  thigh, 

*  Ponzo,  M.,  'Observations  sur  la  direction  des  erreurs  de  localization  dans  les 
espaces  intercostaux,'  Arch.  ital.  de  biol.,  191 1,  56,  193-201. 

*  Ponzo,  M.,  'Studio  della  localizazione  delle  scnsationi  termiche  caldo  e  freddo,' 
Riv.  di  fsicoL,  1913,  9,  393-415. 

*  In  most  of  the  tests  I  have  had  the  assistance  of  Dr.  Mildred  E.  Scheetz,  who 
also  in  my  absence  carried  out  some  of  the  tests  which  are  here  reported.  The  results 
obtained  by  her  did  not  differ  from  those  carried  out  by  me  more  than  those  obtained 
by  me  on  one  day  differed  from  those  obtained  on  a  subsequent  day. 


90  S.  /.  FRANZ 

about  half  way  from  the  knee  and  about  midway  between 
the  middle  and  internal  branches  of  the  anterior  cutaneous 
nerve  of  the  thigh  (branches  of  the  femoral  or  anterior  crural); 
and  {E)  a  corresponding  point  on  the  lateral  portion  of  the 
thigh,  which  is  supposedly  supplied  by  the  lateral  femoral 
cutaneous  nerve.  All  of  the  nerves  supplying  these  parts 
are  relatively  constant  in  direction,  although  in  the  living 
subject  it  is  not  possible  to  determine  their  exact  courses.^ 
Dissection  shows  them  to  be  about  as  constant  in  location 
as  any  other  nerves  of  the  body,  and  they  were  selected 
instead  of  arm  nerves  because  of  the  presumably  lesser 
experience  the  subject  would  have  in  locating  stimuli  along 
their  courses.  It  should  not  be  supposed,  however,  that  the 
location  of  skin  areas  in  relation  to  the  underlying  nerves 
can  be  determined  exactly,  and  that  the  selected  points  are 
definitely  related  to  the  supposed  underlying  nerve  trunks. 
With  respect  to  the  points  at  the  intercostal  spaces,  and 
pari  passu  the  remark  applies  to  the  other  locations,  a  slight 
amount  of  movement  of  the  arm  or  a  slight  twist  of  the  thorax 
will  throw  the  superficial  point  out  of  its  definite  relation 
to  the  intercostal  space,  bringing  it  above  a  rib.^ 

The  stimuli  were  given  by  means  of  a  short  brush,  stiflFer 
than  one  which  I  have  previously  used  for  light  touch  tests, 
and  it  is  certain  that  not  only  was  the  superficial  skin  stimu- 
lated but  also  the  underlying  tissues.  This  would  give  re- 
sults relating  to  the  compound  of  touch  and  pressure  stimuli, 
which  corresponds  well  with  the  conditions  in  the  work  of 
Ponzo.  Twenty  tests  were  made  at  each  point  on  one  day, 
and  the  averages  of  the  tests  are  considered  here.  At  the 
same  time  it  is  possible  to  combine  the  tests  on  different 

^  The  courses  of  these  nerves  may  be  learned  from  almost  any  good  text-book  of 
anatomy. 

*  This  is  a  point  which  must  be  considered  in  dealing  with  the  relations  of  localiza- 
tions to  underlying  nerves.  What  for  example  shall  we  consider  the  nerve  supply  to 
the  skin  overlying  an  intercostal  space  to  be?  Is  it  from  the  nerve  emerging  in  the 
intercostal  space  which  the  skin  covers  when  the  arm  is  held  close  to  the  side  of 
the  body?  Or,  is  it  the  nerve  of  the  space  above,  which  the  skin  covers  when  the  arm 
is  raised  above  the  head  or  in  some  cases  when  the  arm  is  at  a  right  angle  to  the  axis 
of  the  trunk?  In  the  present  work  the  superficial  assumptions  of  Ponzo  have  been 
followed,  but  not  necessarily  accepted. 


CONSTANT  ERROR  9 1 

days  into  suitable  groups  referring  to  the  same  point,  and  to 
make  comparisons  of  the  results. 

Seventh  intercostal  space. — Two  series  of  experiments  were 
made  on  the  left  side,  and  one  on  the  right,  in  the  seventh 
intercostal  space  where  the  space  meets  the  mid-axillary  line. 
Twenty  tests  were  made  in  each  experiment.  The  results 
of  the  calculation  of  the  constant  errors  in  these  experiments 
are  as  follows:  On  the  left,  25,3  mm.  upwards,  3.1  mm. 
toward  the  back  of  the  body;  and  4.0  mm.  downwards,  and 
1.9  mm.  toward  the  back  of  the  body;  on  the  right,  7.5  mm. 
upwards,  and  14.  i  mm.  toward  the  front  of  the  body.  It 
will  be  noted  that  the  error  away  from  the  axillary  line,  toward 
the  front  or  back,  differs  in  the  experiments  on  the  right  and 
left  sides,  and  it  will  also  be  noted  that  the  errors  in  the  two 
series  on  the  left  side  differ  with  respect  to  the  location  of 
the  stimulated  point  in  relation  to  the  upper  and  lower 
(cephalad  and  caudad)  portions  of  the  body.  It  is  apparent 
that  by  the  usual  methods  of  determining  the  constant 
tendency  there  is  not  much  agreement  among  the  three 
experiments.  With  reference  to  the  angles  of  the  average 
constant  error  localizations  in  relation  to  the  mid-axillary 
line  it  may  also  be  said  that  in  the  three  experiments  the 
localizations  are  different.  They  are  respectively  7°,  155°, 
and  61.5°. 

At  the  times  the  tests  were  made  the  directions  of  the 
intercostal  spaces  in  relation  to  the  mid-axillary  line  were 
determined  by  laying  a  finger  upon  the  skin  overlying  the 
space  and  after  having  pressed  the  finger  into  the  space  as 
closely  as  it  would  fit  the  outlines  were  marked  upon  the 
skin  with  a  grease  pencil.  The  center  line  between  the  two 
lines  which  were  marked  was  taken  to  represent  the  direction 
of  the  space,  and  its  angular  direction  in  relation  to  the  mid- 
axillary  line  was  determined,  using  the  portion  of  the  latter 
above  the  point  as  zero  degrees.  In  the  three  experiments 
which  have  been  described  the  directions  which  were  deter- 
mined were  greatly  different,  for  they  were  120°,  137°,  and 
122°  respectively.  At  first  glance  there  appears  the  prob- 
ability of  great  error  in  the  making  of  these  measurements. 


92  S.   /.   FRANZ 

for  it  seems  improbable  that  on  the  same  subject  the  angle 
of  the  ribs  should  differ  by  as  much  as  these  measurements 
dlifer.  To  test  the  matter  the  subject  was  at  a  subsequent 
session  measured  a  number  of  times,  both  by  me  and  by  an 
assistant.  The  grease  pencil  marks  were  obliterated  after 
each  record  was  taken  and  new  marks  were  made  for  each 
determination.  The  results  of  the  measurements  are  as 
follows:  Right  side,  with  the  arm  close  to  the  body,  119° 
and  118°,  with  the  arm  abducted  and  held  above  the  head, 
114°  and  131°,  left  side,  with  the  arm  at  the  side  of  the  body, 
130°  and  120°,  with  the  arm  raised  above  the  head,  128° 
and  125°.  These  measurements  which  were  taken  with 
extra  care  do  not  diifer  from  those  taken  three  months 
previously  more  than  do  the  earlier  corresponding  measure- 
ments from  one  another.  In  other  words  it  appears  that  the 
angular  relation  of  the  seventh  intercostal  space  to  the  mid- 
axillary  line  is  not  constant,  or  that  the  errors  of  measure- 
ment are  large.  The  former  is  what  might  be  expected  from 
what  we  know  of  the  rib  movements  in  connection  with  the 
acts  of  respiration.  At  the  same  time  it  should  also  be 
noted  that  the  angular  directions  of  the  intercostal  spaces 
vary  according  to  the  position  of  the  arms.  This  is  shown 
by  the  series  of  figures  just  given  and  is  further  demonstrated 
by  the  results  of  a  series  of  measurements  on  other  subjects 
on  whom  the  angular  measurements  were  taken  by  Dr. 
Scheetz.     These  measures  are  given  in  Table  I. 

This  table  shows  clearly  the  variations  in  accordance  with 
the  positions  of  the  arms,  the  averages  for  all  completed 
series  (two  each  on  A  and  5,  and  one  each  on  C  and  D) 
being  95°  when  the  arm  is  held  close  to  the  body,  111°  when 
the  hand  is  placed  upon  the  opposite  shoulder,  and  118° 
when  the  arm  Is  raised  above  the  head.  These  variations, 
it  will  be  noted,  are  greater  than  those  found  with  the  subject 
on  whom  the  present  tests  were  made,  and  may  partly  be 
accounted  for  by  differences  In  the  shapes  of  thorax,  and  in 
the  amounts  of  subcutaneous  fat  in  the  four  subjects. 

Assuming,  however,  that  the  angular  measures  first  taken 
on  our  present  subject  (120°,  133°,  and  122°)  are  sufficiently 


CONSTANT  ERROR 


93 


exact,  we  may  examine  the  results  of  the  localizations  by  the 
method  of  Ponzo.  When  we  draw  the  bounding  lines  to 
indicate  the  directions  we  find  for  the  three  series  the  fol- 
lowing: L,  In  the  direction  of  the  space,  5  localizations, 
away  from  the  direction  of  the  space,  15  localizations;  II.,  in 
the  direction  of  the  space,  8,  away  from  the  direction,  12; 
III.,  in  the  direction,  8,  away  from  the  direction,  12.  In  no 
case,  therefore,  did  the  subject  show  a  constant  tendency  to 
localization  in  the  direction  of  the  space,  as  has  been  con- 
tended. 

Table  I 

Angular  Directions  of  the  Seventh  Intercostal  Spaces  in  Relation  to  the 

Mid-axillary  Lines 

Asterisks  denote  that  measurements  were  not  made  in  these  cases. 


Subjects 

Sides  of  Body 

Arm  Near  Body 

Hand  on  Opposite 
Shoulder 

Arm  above  Head 

A 

B 

R. 
L. 
R. 

L. 
R. 
L. 
L. 
R. 
L. 

91 

108 

109 

78 

89 

95 
126 
118 

112 

122 
120 

117 
114 
103 

83 

* 

* 

1X2 
121 

C 

106 

127 
104 
107 

* 

* 

D 

E 

Fourth  Intercostal  Space. — One  series  of  twenty  experi- 
ments on  a  point  in  this  space,  on  the  right  side  four  centi- 
meters from  the  mid-line,  gave  an  average  constant  error 
1 1.8  mm.  downwards,  and  14.  i  mm.  toward  the  mid-line  of 
the  body.  The  angular  relation  of  the  space  to  the  mid- 
body  line  was  found  to  be  approximately  90°.  The  angular 
location  of  the  constant  error  is,  therefore,  within  the  bound- 
aries set  by  Ponzo  (45°  to  135°).  At  a  subsequent  session 
measurements  of  the  angular  relation  of  the  space  to  the 
mid-body  line  gave  78°  on  the  right  side,  and  87°  on  the  left 
side.  In  another  subject  the  angular  relation  was  86°.  It 
will  be  seen,  therefore,  that  the  error  is  close  to  the  lower 
boundary  of  the  angular  limits,  although  within  them. 

When  measured  in  relation  to  the  boundary  lines  it  was 
found  that  14  of  the  localizations  were  within  the  boundaries 


94  S.   7.   FRANZ 

and  6  outside,  although  it  should  also  be  mentioned  that 
only  two  of  the  localizations  were  between  o°  and  90°,  and 
the  remaining  18  were  in  the  space  bounded  by  the  90°  and 
180°  lines. 

Alid-body  Line  at  the  Level  of  the  Nipples. — Two  tests  of 
twenty  experiments  each  were  made  with  the  right  hand 
for  localization  and  one  similar  test  with  the  left  hand  for 
localization.  These  three  tests  show  respectively  the  fol- 
lowing constant  errors:  I.,  7.8  mm.  downwards,  15.2  mm. 
toward  the  left  side;  II.,  0.9  mm.  toward  the  head,  6.1  mm. 
toward  the  left;  III.,  6  mm.  toward  the  head,  3.7  mm.  toward 
the  left.  The  results  in  the  three  series  correspond  as  far 
as  left-sided  localization  is  concerned,  but  do  not  correspond 
with  respect  to  cephalad  or  caudad  localizations.  Since  we 
have  no  definite  knowledge  regarding  the  course  of  the  nerves 
at  this  point  beyond  the  general  belief  that  the  skin  is  prob- 
ably innervated  almost  equally  from  both  sides  of  the  spinal 
cord,  the  results  are  negative.  It  should  be  said,  however, 
that  if  we  believe  in  an  equilateral  innervation  there  is  no 
apparent  reason  for  the  left-sided  localization  constant  error. 

Anterior  Thigh. — The  location  of  the  stimulated  point 
has  already  been  mentioned.  The  results  of  200  experiments, 
20  on  each  leg  on  each  of  five  days,  are  given  in  the  accom- 
panying table  (Table  11.)  which  shows  the  average  errors  of 
localization,  the  constant  errors  centralwards  or  distalwards, 
and  to  the  right  or  to  the  left.  The  results  of  the  calculation 
of  the  same  results  by  the  rougher  method  of  angular  limits 
are  also  shown  in  Table  III.  It  will  be  seen  that  the  constant 
errors  in  the  five  series  do  not  correspond.  In  one  test  the 
average  constant  error  lies  to  the  left,  in  another  test  it  lies 
to  the  right;  in  one  it  is  toward  the  abdomen,  in  another  it 
is  toward  the  foot.  At  the  same  time  it  will  be  observed 
that  there  are  great  variations  in  the  localizations  in  relation 
to  the  angular  measurements,  and  that,  on  the  assumption 
of  a  direction  of  nerve  from  355°  to  175°,  the  constant  error 
is  located  within  the  angular  limits  in  only  seven  of  the  ten 
experiments.  The  totals  of  the  100  experiments  on  the 
right  and   the   100  experiments  on  the  left  show  that  the 


CONSTANT  ERROR 


95 


general  direction  of  localization  is  in  the  nerve  direction,  if 
we  can  use  the  method  of  angular  limits  for  the  determination 
of  the  constant  error.  This  tendency  to  location  in  the 
supposed  direction  of  the  nerve  is,  however,  not  very  large, 
for  there  is  only  a  superiority  of  50  per  cent,  in  the  localiza- 
tions in  the  direction  as  compared  with  those  at  right  angle  to 
the  direction  (viz.,  120  :  80). 


Table  II 

Average  and  Constant  Errors  on  the  Right  Anterior  Thigh. 
20  Experiments  on  Each  Day 

Constant  errors  calculated  by  the  usual  method. 


Serial  Days 

Averages 

I 

2 

1            3 

4 

5 

Av.  error 

C.E.tl   

24-3 

ti9i 
0 
0 

17-5 

t  IO-5 
0 
0 

12.0 
4,6.3 

<-i.3 

1     168.5 

20.0 

4,13.8 

-^5-3 
159.0 

17.0 
4,1.6 

-»9-7 
99.0 

18.2 

t40 

->2.8 

c.e.;^ 

C.E.  degrees 

35-0 

Average  and  Constant  Errors  on  the  Left  Anterior  Thigh. 
20  Experiments  on  Each  Day 


Av.  error.  . .  . 

C.E.  U  .  . . . 
C.E.  ^  .... 
C.E.  degrees. 


17.8 

13.0 

12.S 

14.0 

25.0 

t3-3 

4,2.8 

4,4-8 

4,  2.7 

t4-0 

^2.8 

-»i-7 

^2.1 

^7-5 

->0.2 

320.0 

149.0 

203-5 

250.0 

3.0 

I6.S 

4,1.5 

<-2.I 

235-0 


Table  III 

Constant  Errors  Determined  by  Method  of  Angular  Limits 


Serial  Days 

I 

2 

3 
4 

5 


Right  Side 
Direction  of  Nerve 

13 
II 

14 
10 

li 


Totals 63 

Left  Side 


12 
15 


Opposite  Direction 

7 

9 

6 
10 
_5 

37 


10 

12 

8 

S 
8 


Totals 57 


43 


96 


S.  /.  FRANZ 


Table  IV 

Average  and  Constant  Errors  on  the  Right  Lateral  Thigh. 
20  Experiments  on  Each  Day 

Constant  errors  calculated  bv  the  usual  method. 


Serial  Days 

I 

2 

3 

4 

5 

Averages 

Av.  error 

C.E.  ti  

C.E.  ^ 

17.0 

13-8 

-^9.1 

67.0 

13-3 
4.2.8 

231-5 

14.0 

t8.5 

-»3-7 
24.0 

33-8 

4.5.2 

->34-i 
98.5 

54-5 
tio.3 
-^50.6 

78.5 

26.5 
t2.9 

^18.8 

C.E.  degrees 

82.0 

Average  and  Constant  Errors  on  the  Left  Lateral  Thigh. 
20  Experiments  on  Each  Day 


Av.  error. . .  . 

C.E.  U  .  .  .  - 
C.E.  ?±  .  . .  . 
C.E.  degrees. 


22.8 

14.8 

Jr  iS-3 

Jf2.8 

<-I2.3 

^7-5 

219.0 

290.5 

16.0 

t2.8 

^5-7 
297.0 


23-3 

28.3 

tS-9 

t4-2 

<-  8.8 

.^22.8 

287.0 

280.0 

21.0 

to.i 

<-i3-4 
270.0 


Table  V 

Constant  Errors  Determined  by  Method  of  Angular  Limits 
When  a  point  has  been  on  a  line  it  has  been  calculated  as  half  each  way. 


Right  Side 

Serial  Days 

Direction  of  Nerve 

Opposite  Direction 

I 

12 

8 

2 
3 

4 

9-5 

10.S 

0 

10.S 

9-5 
20 

5 

0 

20 

Totals 

32 

Lejt  Side 

68 

I 

2 

3 

4 
5 

10.5 
S-5 
7 

3-S 
5 

9-5 
14.5 

13 

16.S 

IS 

Totals 

31-5 

68.5 

Right  Lateral  Thigh. — The  nerve  supplying  this  portion 
of  the  body  is  very  constant  in  direction  in  cadavers,  following 
an  almost  straight  line  from  the  crest  of  the  ileum  to  the 
middle  of  the  knee,  in  other  words  from  0°  to  180°.     The  re- 


CONSTANT  ERROR  97 

suits  of  five  tests  on  different  days  on  the  two  legs  on  the 
selected  points,  200  experiments  in  all,  are  given  in  Table  IV., 
and  the  results  of  the  calculation  by  the  method  of  angular 
limits  are  given  in  Table  V. 

In  these  tables  it  will  be  observed  that  the  constant  errors 
in  the  individual  tests  differ  greatly.  In  some  there  is  an 
apparent  tendency  to  locate  toward  the  pelvis,  in  others 
toward  the  knee;  in  one  there  is  a  tendency  to  locate  toward 
the  dorsal  surface  and  in  the  other  nine  toward  the  anterior 
surface  of  the  leg.  The  angular  relations  of  the  constant 
error  determinations  to  the  supposed  nerve  course  in  these 
ten  series  greatly  differ,  ranging  from  24°  to  231°  on  the 
right  leg,  and  from  219°  to  297°  on  the  left  leg.  Within 
the  artificial  angular  limits  there  is  only  one  constant  error 
direction  on  the  right  and  none  on  the  left  side,  four  on  the 
right  and  five  on  the  left  being  outside  of  the  supposed  angular 
directions. 

In  only  three  tests  is  there  a  predominance  of  localizations 
in  the  direction  of  the  artificially  set  angular  limits,  and  in 
the  other  seven  tests  there  is  a  superiority  of  localization  in 
the  spaces  at  right  angle  to  the  artificially  set  directions. 
For  the  total  of  ten  tests,  therefore,  there  is  a  superiority  in 
direction  away  from  the  space  amounting  to  over  100  per 
cent. 

Summary. — The  method  of  calculation  of  constant  error 
by  angular  limits  is  too  inexact  to  warrant  its  use  except  as  a 
possible  qualitative  method  for  preliminary  work.  The 
constant  error  tendency  in  the  five  locations  selected  for  the 
present  series  of  tests  is  in  only  one  place  in  the  supposed 
direction  of  the  innervating  nerve,  whether  this  tendency 
be  measured  by  the  usual  and  more  exact  means  or  by  the 
method  of  angular  limits  used  by  Ponzo.  Conclusions 
regarding  the  constancy  of  direction  of  constant  errors  must 
be  radically  changed  to  conform  to  the  facts. 

One  possible  objection  may  be  raised  to  the  present  series 
of  results.  This  is  that  they  have  been  obtained  with  only 
one  subject.  This  objection  loses  its  force  In  view  of  the 
widespread    generalizations    which    have    been    made,    for   It 


98 


S.  /.  FRANZ 


becomes,  apparent  that  if  the  conclusions  set  forth  by  the 
ItaHan  investigator  are  not  applicable  to  other  than  his  own 
subjects  they  cannot  be  accepted  as  general.  I  am  not 
willing,  however,  to  admit  that  Ponzo's  conclusions  have  been 
founded  upon  the  utilization  of  the  best  methods,  and  in 
fact  it  is  amply  demonstrated  that  the  method  employed  by 
him  is  so  faulty  that  its  use  is  unjustified. 


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